x=6+(1/x)

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Solution for x=6+(1/x) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x = 1/x+6 // - 1/x+6

x-(1/x)-6 = 0

x-x^-1-6 = 0

1*x^1-1*x^-1-6*x^0 = 0

(1*x^2-6*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-6*x^1-1*x^0) = 0

x^1

x^2-6*x-1 = 0

x^2-6*x-1 = 0

DELTA = (-6)^2-(-1*1*4)

DELTA = 40

DELTA > 0

x = (40^(1/2)+6)/(1*2) or x = (6-40^(1/2))/(1*2)

x = (2*10^(1/2)+6)/2 or x = (6-2*10^(1/2))/2

x in { (6-2*10^(1/2))/2, (2*10^(1/2)+6)/2} 

x in { (6-2*10^(1/2))/2, (2*10^(1/2)+6)/2 }

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